Feasibility Problem in CVX

1

Hi,
I am running following code in CVX.This is feasibility problem and my aim is to get positive definite matrix § which satisfies given constraints.
Assuming I got one such P matrix , but any positive multiple of matrix P will also satisfy given constraints, that means solution is not unique.
How does CVX program decide final value of P?

Thanks in advance

cvx_begin sdp 
    cvx_precision best
    variable P(size(Ghat))   hermitian   
    minimize 0
    subject to   
    P >= 0.00000001*eye(2)
    for i=1:count-1
       ( (Grandom{i})'*P*X+X'*P*(Grandom{i})) >= 0
    end
cvx_end
2

The method for deciding the final solution depends entirely on the solver. But frankly, your model suffers from a common problem with homogeneous constraints—don’t be surprised if solvers think P=0 is an entirely acceptable solution numerically. Your constraint P >= 0.00000001*eye(2) is not effective. Please see this section of the users’ guide. In particular: Note that the bound needs to be large enough so that the underlying solver considers it numerically significant.

3

Thanks for you reply.
it is not giving P=0 solution. Sedumi solver is giving solution like P=10^94 *eye(2), which is totally absurd value.

4

Well, if you don’t want it to be absurd, then you will need to add some constraints to make it so. Perhaps you can bound the trace of P, for instance, or even minimize it—but if you do, replace P >= 0.00000001*eye(2) with something numerically significant like P >= eye(2).